{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 机器学习工程师纳米学位\n",
    "## 模型评价与验证\n",
    "## 项目 1: 预测波士顿房价\n",
    "\n",
    "\n",
    "欢迎来到机器学习的预测波士顿房价项目！在此文件中，有些示例代码已经提供给你，但你还需要实现更多的功能来让项目成功运行。除非有明确要求，你无须修改任何已给出的代码。以**编程练习**开始的标题表示接下来的内容中有需要你必须实现的功能。每一部分都会有详细的指导，需要实现的部分也会在注释中以**TODO**标出。请仔细阅读所有的提示！\n",
    "\n",
    "除了实现代码外，你还**必须**回答一些与项目和实现有关的问题。每一个需要你回答的问题都会以**'问题 X'**为标题。请仔细阅读每个问题，并且在问题后的**'回答'**文字框中写出完整的答案。你的项目将会根据你对问题的回答和撰写代码所实现的功能来进行评分。\n",
    "\n",
    ">**提示：**Code 和 Markdown 区域可通过 **Shift + Enter** 快捷键运行。此外，Markdown可以通过双击进入编辑模式。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 第一步. 导入数据\n",
    "在这个项目中，你将利用马萨诸塞州波士顿郊区的房屋信息数据训练和测试一个模型，并对模型的性能和预测能力进行测试。通过该数据训练后的好的模型可以被用来对房屋做特定预测---尤其是对房屋的价值。对于房地产经纪等人的日常工作来说，这样的预测模型被证明非常有价值。\n",
    "\n",
    "此项目的数据集来自[UCI机器学习知识库(数据集已下线)](https://archive.ics.uci.edu/ml/datasets.html)。波士顿房屋这些数据于1978年开始统计，共506个数据点，涵盖了麻省波士顿不同郊区房屋14种特征的信息。本项目对原始数据集做了以下处理：\n",
    "- 有16个`'MEDV'` 值为50.0的数据点被移除。 这很可能是由于这些数据点包含**遗失**或**看不到的值**。\n",
    "- 有1个数据点的 `'RM'` 值为8.78. 这是一个异常值，已经被移除。\n",
    "- 对于本项目，房屋的`'RM'`， `'LSTAT'`，`'PTRATIO'`以及`'MEDV'`特征是必要的，其余不相关特征已经被移除。\n",
    "- `'MEDV'`特征的值已经过必要的数学转换，可以反映35年来市场的通货膨胀效应。\n",
    "\n",
    "运行下面区域的代码以载入波士顿房屋数据集，以及一些此项目所需的 Python 库。如果成功返回数据集的大小，表示数据集已载入成功。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Boston housing dataset has 489 data points with 4 variables each.\n"
     ]
    }
   ],
   "source": [
    "# Import libraries necessary for this project\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn.model_selection import ShuffleSplit\n",
    "\n",
    "# Import supplementary visualizations code visuals.py\n",
    "import visuals as vs\n",
    "\n",
    "# Pretty display for notebooks\n",
    "%matplotlib inline\n",
    "\n",
    "# Load the Boston housing dataset\n",
    "data = pd.read_csv('housing.csv')\n",
    "prices = data['MEDV']\n",
    "features = data.drop('MEDV', axis = 1)\n",
    "    \n",
    "# Success\n",
    "print(\"Boston housing dataset has {} data points with {} variables each.\".format(*data.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 第二步. 分析数据\n",
    "在项目的第一个部分，你会对波士顿房地产数据进行初步的观察并给出你的分析。通过对数据的探索来熟悉数据可以让你更好地理解和解释你的结果。\n",
    "\n",
    "由于这个项目的最终目标是建立一个预测房屋价值的模型，我们需要将数据集分为**特征(features)**和**目标变量(target variable)**。\n",
    "- **特征** `'RM'`， `'LSTAT'`，和 `'PTRATIO'`，给我们提供了每个数据点的数量相关的信息。\n",
    "- **目标变量**：` 'MEDV'`，是我们希望预测的变量。\n",
    "\n",
    "他们分别被存在 `features` 和 `prices` 两个变量名中。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习 1：基础统计运算\n",
    "你的第一个编程练习是计算有关波士顿房价的描述统计数据。我们已为你导入了 ` NumPy `，你需要使用这个库来执行必要的计算。这些统计数据对于分析模型的预测结果非常重要的。\n",
    "在下面的代码中，你要做的是：\n",
    "- 计算 `prices` 中的 `'MEDV'` 的最小值、最大值、均值、中值和标准差；\n",
    "- 将运算结果储存在相应的变量中。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statistics for Boston housing dataset:\n",
      "\n",
      "Minimum price: $105000.00\n",
      "Maximum price: $1024800.00\n",
      "Mean price: $454342.94\n",
      "Median price $438900.00\n",
      "Standard deviation of prices: $165171.13\n"
     ]
    }
   ],
   "source": [
    "# TODO: Minimum price of the data\n",
    "minimum_price = np.min(prices)\n",
    "\n",
    "# TODO: Maximum price of the data\n",
    "maximum_price = np.max(prices)\n",
    "\n",
    "# TODO: Mean price of the data\n",
    "mean_price = np.mean(prices)\n",
    "\n",
    "# TODO: Median price of the data\n",
    "median_price = np.median(prices)\n",
    "\n",
    "# TODO: Standard deviation of prices of the data\n",
    "std_price = np.std(prices)\n",
    "\n",
    "# Show the calculated statistics\n",
    "print(\"Statistics for Boston housing dataset:\\n\")\n",
    "print(\"Minimum price: ${:.2f}\".format(minimum_price)) \n",
    "print(\"Maximum price: ${:.2f}\".format(maximum_price))\n",
    "print(\"Mean price: ${:.2f}\".format(mean_price))\n",
    "print(\"Median price ${:.2f}\".format(median_price))\n",
    "print(\"Standard deviation of prices: ${:.2f}\".format(std_price))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 1 - 特征观察\n",
    "\n",
    "如前文所述，本项目中我们关注的是其中三个值:`'RM'`、`'LSTAT'` 和`'PTRATIO'`，对每一个数据点:\n",
    "- `'RM'` 是该地区中每个房屋的平均房间数量；\n",
    "- `'LSTAT'` 是指该地区有多少百分比的业主属于是低收入阶层（有工作但收入微薄）；\n",
    "- `'PTRATIO'` 是该地区的中学和小学里，学生和老师的数目比（`学生/老师`）。\n",
    "\n",
    "_凭直觉，上述三个特征中对每一个来说，你认为增大该特征的数值，`'MEDV'`的值会是**增大**还是**减小**呢？每一个答案都需要你给出理由。_\n",
    "\n",
    "**提示：**你预期一个`'RM'` 值是6的房屋跟`'RM'` 值是7的房屋相比，价值更高还是更低呢？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 1 - 回答：\n",
    "1. RM增加，'MEDV'的值也会增加，每个房屋的平均房间数量增加代表着该房屋的平均面积也会有所上升，同时房间数量越多代表其可居住能力越高，理论上其价格也会随之增大；\n",
    "2. LSTAT增加，代表着该地区业主中低收入阶层的占比增加，同理代表该地区整体消费能力的下降，那么'MEDV'也理应随之减小；\n",
    "3. PIRATIO增加为该地区学生相对教师占比更高,代表该区域老师需求量增加，教师需求量增加自然代表着住房的需求增加，按照供求关系，'MEDV'也会增大。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 第三步. 建立模型\n",
    "在项目的第三步中，你需要了解必要的工具和技巧来让你的模型进行预测。用这些工具和技巧对每一个模型的表现做精确的衡量可以极大地增强你预测的信心。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习2：定义衡量标准\n",
    "如果不能对模型的训练和测试的表现进行量化地评估，我们就很难衡量模型的好坏。通常我们会定义一些衡量标准，这些标准可以通过对某些误差或者拟合程度的计算来得到。在这个项目中，你将通过运算[决定系数](https://en.wikipedia.org/wiki/Coefficient_of_determination) $R^2$ 来量化模型的表现。模型的决定系数是回归分析中十分常用的统计信息，经常被当作衡量模型预测能力好坏的标准。\n",
    "\n",
    "$R^2$ 的数值范围从0至1，表示**目标变量**的预测值和实际值之间的相关程度平方的百分比。一个模型的 $R^2$ 值为0还不如直接用**平均值**来预测效果好；而一个 $R^2$ 值为1的模型则可以对目标变量进行完美的预测。从0至1之间的数值，则表示该模型中目标变量中有百分之多少能够用**特征**来解释。模型也可能出现负值的 $R^2$，这种情况下模型所做预测有时会比直接计算目标变量的平均值差很多。\n",
    "\n",
    "在下方代码的 `performance_metric` 函数中，你要实现：\n",
    "- 使用 `sklearn.metrics` 中的 [`r2_score`](http://scikit-learn.org/stable/modules/generated/sklearn.metrics.r2_score.html) 来计算 `y_true` 和 `y_predict` 的 $R^2$ 值，作为对其表现的评判。\n",
    "- 将他们的表现评分储存到 `score` 变量中。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# TODO: Import 'r2_score'\n",
    "from sklearn.metrics import r2_score\n",
    "\n",
    "def performance_metric(y_true, y_predict):\n",
    "    \"\"\" Calculates and returns the performance score between \n",
    "        true and predicted values based on the metric chosen. \"\"\"\n",
    "    \n",
    "    # TODO: Calculate the performance score between 'y_true' and 'y_predict'\n",
    "    score = r2_score(y_true,y_predict)\n",
    "    \n",
    "    # Return the score\n",
    "    return score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 2 - 拟合程度\n",
    "\n",
    "假设一个数据集有五个数据且一个模型做出下列目标变量的预测：\n",
    "\n",
    "| 真实数值 | 预测数值 |\n",
    "| :-------------: | :--------: |\n",
    "| 3.0 | 2.5 |\n",
    "| -0.5 | 0.0 |\n",
    "| 2.0 | 2.1 |\n",
    "| 7.0 | 7.8 |\n",
    "| 4.2 | 5.3 |\n",
    "*你觉得这个模型已成功地描述了目标变量的变化吗？如果成功，请解释为什么，如果没有，也请给出原因。*  \n",
    "\n",
    "**提示1**：运行下方的代码，使用 `performance_metric` 函数来计算 `y_true` 和 `y_predict` 的决定系数。\n",
    "\n",
    "**提示2**：$R^2$ 分数是指可以从自变量中预测的因变量的方差比例。 换一种说法：\n",
    "\n",
    "* $R^2$ 为0意味着因变量不能从自变量预测。\n",
    "* $R^2$ 为1意味着可以从自变量预测因变量。\n",
    "* $R^2$ 在0到1之间表示因变量可预测的程度。\n",
    "* $R^2$ 为0.40意味着 Y 中40％的方差可以从 X 预测。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model has a coefficient of determination, R^2, of 0.923.\n"
     ]
    }
   ],
   "source": [
    "# Calculate the performance of this model\n",
    "score = performance_metric([3, -0.5, 2, 7, 4.2], [2.5, 0.0, 2.1, 7.8, 5.3])\n",
    "print(\"Model has a coefficient of determination, R^2, of {:.3f}.\".format(score))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 2 - 回答:\n",
    "该模型已成功描述目标变量变化，因为该模型的R2系数为0.923，代表该模型有92%的描述目标变量的变化。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习 3: 数据分割与重排\n",
    "接下来，你需要把波士顿房屋数据集分成训练和测试两个子集。通常在这个过程中，数据也会被重排列，以消除数据集中由于顺序而产生的偏差。\n",
    "在下面的代码中，你需要\n",
    "\n",
    "* 使用 `sklearn.model_selection` 中的 `train_test_split`， 将 `features` 和 `prices` 的数据都分成用于训练的数据子集和用于测试的数据子集。\n",
    "  - 分割比例为：80%的数据用于训练，20%用于测试；\n",
    "  - 选定一个数值以设定 `train_test_split` 中的 `random_state` ，这会确保结果的一致性；\n",
    "* 将分割后的训练集与测试集分配给 `X_train`, `X_test`, `y_train` 和 `y_test`。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training and testing split was successful.\n"
     ]
    }
   ],
   "source": [
    "# TODO: Import 'train_test_split'\n",
    "from sklearn.model_selection import train_test_split\n",
    "# TODO: Shuffle and split the data into training and testing subsets\n",
    "X_train, X_test, y_train, y_test = train_test_split(features, prices, test_size=0.2, random_state=0)\n",
    "\n",
    "# Success\n",
    "print(\"Training and testing split was successful.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 3 - 训练及测试\n",
    "*将数据集按一定比例分为训练用的数据集和测试用的数据集对学习算法有什么好处？*\n",
    "\n",
    "*如果用模型已经见过的数据，例如部分训练集数据进行测试，又有什么坏处？*\n",
    "\n",
    "**提示：** 如果没有数据来对模型进行测试，会出现什么问题？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 3 - 回答:\n",
    "\n",
    "1. 将数据分为训练集及测试集，训练集用于进行模型的构建，测试集用于检验构建好的模型，评估模型的准确率，将数据集按一定比例分开，可以在尽可能使模型拟合程度贴近整体样本的情况下，判断该模型对未知数据的预测能力；\n",
    "2. 将模型已经见过的数据用于测试，会导致测试集的测试结果无法用于评估该模型的预测能力。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 第四步. 分析模型的表现\n",
    "在项目的第四步，我们来看一下不同参数下，模型在训练集和验证集上的表现。这里，我们专注于一个特定的算法（带剪枝的决策树，但这并不是这个项目的重点），和这个算法的一个参数 `'max_depth'`。用全部训练集训练，选择不同`'max_depth'` 参数，观察这一参数的变化如何影响模型的表现。画出模型的表现来对于分析过程十分有益。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 学习曲线\n",
    "下方区域内的代码会输出四幅图像，它们是一个决策树模型在不同最大深度下的表现。每一条曲线都直观得显示了随着训练数据量的增加，模型学习曲线的在训练集评分和验证集评分的变化，评分使用决定系数 $R^2$。曲线的阴影区域代表的是该曲线的不确定性（用标准差衡量）。\n",
    "\n",
    "运行下方区域中的代码，并利用输出的图形回答下面的问题。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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WW/uwfXsCxsD27QncemsfZs1qFguNl1WrVgUGDBgw9JJLLuk9dOjQIZs2bYq/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\ngQ+SzMzMzMzMCv4HfNG01tSgPdIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x3875190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Produce learning curves for varying training set sizes and maximum depths\n",
    "vs.ModelLearning(features, prices)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 4 - 学习曲线\n",
    "* 选择上述图像中的其中一个，并给出其最大深度。\n",
    "* 随着训练数据量的增加，训练集曲线的评分有怎样的变化？验证集曲线呢？\n",
    "* 如果有更多的训练数据，是否能有效提升模型的表现呢？\n",
    "\n",
    "**提示：**学习曲线的评分是否最终会收敛到特定的值？一般来说，你拥有的数据越多，模型表现力越好。但是，如果你的训练和测试曲线以高于基准阈值的分数收敛，这是否有必要？基于训练和测试曲线已经收敛的前提下，思考添加更多训练点的优缺点。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 4 - 回答:\n",
    "\n",
    "当max_depth为3时，随着训练数据量的增加，训练集取消的评分呈现下降逐渐趋向于0.8，验证集曲线从数据量50时评分接近0.6，随着数据集的增加逐渐向0.8靠近；随着训练数据的增加，模型的表现相对提升，达到一定数量集后再增加数量集评分基本趋近特定值，提升空间将降低。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 复杂度曲线\n",
    "下列代码内的区域会输出一幅图像，它展示了一个已经经过训练和验证的决策树模型在不同最大深度条件下的表现。这个图形将包含两条曲线，一个是训练集的变化，一个是验证集的变化。跟**学习曲线**相似，阴影区域代表该曲线的不确定性，模型训练和测试部分的评分都用的 `performance_metric` 函数。\n",
    "\n",
    "**运行下方区域中的代码，并利用输出的图形并回答下面的问题5与问题6。**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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J76KIeIGfA+8DtgLPicj9xphXsza7GLjXGHOTiBwKPAjMKqVdEw5jbHWDjRut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\nROKKEp+IiMQVJT4REYkr/w/GkizpLOLDHwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12332eb0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vs.ModelComplexity(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 5 - 偏差（bias）与方差（variance）之间的权衡取舍\n",
    "* 当模型以最大深度 1训练时，模型的预测是出现很大的偏差还是出现了很大的方差？\n",
    "* 当模型以最大深度10训练时，情形又如何呢？\n",
    "* 图形中的哪些特征能够支持你的结论？\n",
    "  \n",
    "**提示：** 高偏差表示欠拟合（模型过于简单），而高方差表示过拟合（模型过于复杂，以至于无法泛化）。考虑哪种模型（深度1或10）对应着上述的情况，并权衡偏差与方差。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 5 - 回答:\n",
    "\n",
    "根据r2_score的计算公式为r2_score = 1 - bias/variance,因此由上图可知当depth为1时r2_score最低，代表bias/variance最大，因此可知此时为高偏差，即欠拟合；当depth为10时此时Training score对应最高，即此时bias/variance最小，因此可知此时为高方差，及过拟合。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 6- 最优模型的猜测\n",
    "* 结合问题 5 中的图，你认为最大深度是多少的模型能够最好地对未见过的数据进行预测？\n",
    "* 你得出这个答案的依据是什么？\n",
    "\n",
    "**提示**：查看问题5上方的图表，并查看模型在不同 `depth`下的验证分数。随着深度的增加模型的表现力会变得更好吗？我们在什么情况下获得最佳验证分数而不会使我们的模型过度复杂？请记住，奥卡姆剃刀：“在竞争性假设中，应该选择假设最少的那一个。”"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 6 - 回答:\n",
    "\n",
    "1. 当depth为4时模型对未见过的数据预测效果最好，首先根据问题5图形呈现当depth为3时Training score与validation score随着数据集的增加逐渐接近特定值，且该值处于高点，而当depth为6时，两个score随着数据集增加同样都处于高点，但是已经出现了难以趋向相同特点值的状况及过拟合的状况发生，因此最优depth应该处于4-6之间。\n",
    "1. 再次观察问题6对应图表，我们可以看出Training score随着depth增加逐渐上升，但是validation score确在depth为4之后开始呈现下降的趋势，因此当depth为4时，训练模式的验证拟合度最好，且训练得分与验证得分都为高点，因此判断当depth为4时对未见过的数据预测性最高。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 第五步. 评估模型的表现\n",
    "在项目的最后一节中，你将构建一个模型，并使用 `fit_model` 中的优化模型去预测客户特征集。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 7- 网格搜索（Grid Search）\n",
    "* 什么是网格搜索法？\n",
    "* 如何用它来优化模型？\n",
    "\n",
    "**提示**：在解释网格搜索算法时，首先要理解我们为什么使用网格搜索算法，以及我们使用它的最终目的是什么。为了使你的回答更具有说服力，你还可以给出一个模型中可以使用此方法进行优化参数的示例。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 7 - 回答:\n",
    "\n",
    "1. 网格搜索法指的是在指定的范围内自动搜索具有不同超参数的不同模型组合；\n",
    "2. 通过网格搜索法尝试所有超参的组合，然后进行交叉验证，找到使交叉验证精确度最高的参数组合，得到最好的预测位置数据的模型。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 8 - 交叉验证\n",
    "- 什么是K折交叉验证法（k-fold cross-validation）？\n",
    "- [GridSearchCV](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html) 是如何结合交叉验证来完成对最佳参数组合的选择的？\n",
    "- [GridSearchCV](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html) 中的`'cv_results_'`属性能告诉我们什么？\n",
    "- 网格搜索为什么要使用K折交叉验证？K折交叉验证能够避免什么问题？\n",
    "\n",
    "**提示**：在解释k-fold交叉验证时，一定要理解'k'是什么，和数据集是如何分成不同的部分来进行训练和测试的，以及基于'k'值运行的次数。\n",
    "在考虑k-fold交叉验证如何帮助网格搜索时，你可以使用特定的数据子集来进行训练与测试有什么缺点，以及K折交叉验证是如何帮助缓解这个问题。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 8 - 回答：\n",
    "\n",
    "1. K折交叉验证法：由于现实数据有限，将训练数据进行分为K组，K-1组作为训练集，1组作为验证集，对模型进行K次训练，泛化误差为K次的平均，最终选择平均误差率最低的模型；\n",
    "2. GridSearchCV进行自动调参，通过交叉验证，计算不同参数组合对应交叉验证的结果，然后根据返回测试得分排名最高的参数组合，即最佳参数组合；\n",
    "3. 以本次训练为例，该决策树模型，超参depth取1-10，cv_result_属性包含不同参数取值时的平均训练得分，平均测试得分，K折验证过程每次验证对应的训练得分与测试得分，包括训练及测试得分的方差，还可以得到模型训练所需要的时间及每次训练匹配时间的方差；\n",
    "4. 由于实际情况中数据集样本数较少，不适用交叉验证的方法会导致训练结果难以代表整体样本的分布情况，测试结果的拟合度也相对较低。交叉验证通过将数据分为K份，依次使用其中1份数据作为测试集，其余用于训练，K次训练，得出平均拟合状况，可以降低由于数据集样本较小造成的影响。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习 4：拟合模型\n",
    "在这个练习中，你将需要将所学到的内容整合，使用**决策树算法**训练一个模型。为了得出的是一个最优模型，你需要使用网格搜索法训练模型，以找到最佳的 `'max_depth'` 参数。你可以把`'max_depth'` 参数理解为决策树算法在做出预测前，允许其对数据提出问题的数量。决策树是**监督学习算法**中的一种。\n",
    "\n",
    "另外，你会发现在实现的过程中是使用`ShuffleSplit()`作为交叉验证的另一种形式（参见'cv_sets'变量）。虽然它不是你在问题8中描述的K-fold交叉验证方法，但它同样非常有用！下面的`ShuffleSplit()`实现将创建10个('n_splits')混洗集合，并且对于每个混洗集，数据的20％（'test_size'）将被用作验证集合。当您在实现代码的时候，请思考一下它与`K-fold cross-validation`的不同与相似之处。\n",
    "\n",
    "请注意，`ShuffleSplit` 在 `Scikit-Learn` 版本0.17和0.18中有不同的参数。对于下面代码单元格中的 `fit_model` 函数，您需要实现以下内容：\n",
    "\n",
    "1. **定义 `'regressor'` 变量**: 使用  `sklearn.tree` 中的 [`DecisionTreeRegressor`](http://scikit-learn.org/stable/modules/generated/sklearn.tree.DecisionTreeRegressor.html) 创建一个决策树的回归函数;\n",
    "2. **定义 `'params'` 变量**: 为 `'max_depth'` 参数创造一个字典，它的值是从1至10的数组;\n",
    "3. **定义 `'scoring_fnc'` 变量**: 使用 `sklearn.metrics` 中的 [`make_scorer`](http://scikit-learn.org/stable/modules/generated/sklearn.metrics.make_scorer.html)  创建一个评分函数。将 `‘performance_metric’` 作为参数传至这个函数中；\n",
    "4. **定义 `'grid'` 变量**: 使用 `sklearn.model_selection` 中的 [`GridSearchCV`](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html) 创建一个网格搜索对象；将变量`'regressor'`, `'params'`, `'scoring_fnc'`和 `'cross_validator'` 作为参数传至这个对象构造函数中；\n",
    "\n",
    "  \n",
    "如果你对 Python 函数的默认参数定义和传递不熟悉，可以参考这个MIT课程的[视频](http://cn-static.udacity.com/mlnd/videos/MIT600XXT114-V004200_DTH.mp4)。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# TODO: Import 'make_scorer', 'DecisionTreeRegressor', and 'GridSearchCV'\n",
    "\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "from sklearn.metrics import make_scorer\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "\n",
    "def fit_model(X, y):\n",
    "    \"\"\" Performs grid search over the 'max_depth' parameter for a \n",
    "        decision tree regressor trained on the input data [X, y]. \"\"\"\n",
    "    \n",
    "    # Create cross-validation sets from the training data\n",
    "    # sklearn version 0.18: ShuffleSplit(n_splits=10, test_size=0.1, train_size=None, random_state=None)\n",
    "    # sklearn versiin 0.17: ShuffleSplit(n, n_iter=10, test_size=0.1, train_size=None, random_state=None)\n",
    "    cv_sets = ShuffleSplit(n_splits=10, test_size=0.20, random_state=42)\n",
    "    \n",
    "    # TODO: Create a decision tree regressor object\n",
    "    regressor = DecisionTreeRegressor()\n",
    "\n",
    "    # TODO: Create a dictionary for the parameter 'max_depth' with a range from 1 to 10\n",
    "    params = {'max_depth':range(1,10)}\n",
    "\n",
    "    # TODO: Transform 'performance_metric' into a scoring function using 'make_scorer' \n",
    "    scoring_fnc = make_scorer(performance_metric)\n",
    "\n",
    "    # TODO: Create the grid search cv object --> GridSearchCV()\n",
    "    # Make sure to include the right parameters in the object:\n",
    "    # (estimator, param_grid, scoring, cv) which have values 'regressor', 'params', 'scoring_fnc', and 'cv_sets' respectively.\n",
    "    grid = GridSearchCV(regressor, param_grid= params, scoring= scoring_fnc, cv = cv_sets)\n",
    "\n",
    "    # Fit the grid search object to the data to compute the optimal model\n",
    "    grid = grid.fit(X, y)\n",
    "\n",
    "    # Return the optimal model after fitting the data\n",
    "    return grid.best_estimator_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 第六步. 做出预测\n",
    "当我们用数据训练出一个模型，它现在就可用于对新的数据进行预测。在决策树回归函数中，模型已经学会对新输入的数据*提问*，并返回对**目标变量**的预测值。你可以用这个预测来获取数据未知目标变量的信息，这些数据必须是不包含在训练数据之内的。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 9 - 最优模型\n",
    "*最优模型的最大深度（maximum depth）是多少？此答案与你在**问题 6**所做的猜测是否相同？*\n",
    "\n",
    "运行下方区域内的代码，将决策树回归函数代入训练数据的集合，以得到最优化的模型。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter 'max_depth' is 4 for the optimal model.\n"
     ]
    }
   ],
   "source": [
    "# Fit the training data to the model using grid search\n",
    "reg = fit_model(X_train, y_train)\n",
    "\n",
    "# Produce the value for 'max_depth'\n",
    "print(\"Parameter 'max_depth' is {} for the optimal model.\".format(reg.get_params()['max_depth']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 9 - 回答：\n",
    "\n",
    "1. 最优模型的最大深度为4，与问题6中所做的猜测一致。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 10 - 预测销售价格\n",
    "想像你是一个在波士顿地区的房屋经纪人，并期待使用此模型以帮助你的客户评估他们想出售的房屋。你已经从你的三个客户收集到以下的资讯:\n",
    "\n",
    "| 特征 | 客戶 1 | 客戶 2 | 客戶 3 |\n",
    "| :---: | :---: | :---: | :---: |\n",
    "| 房屋内房间总数 | 5 间房间 | 4 间房间 | 8 间房间 |\n",
    "| 社区贫困指数（％被认为是贫困阶层） | 17% | 32% | 3% |\n",
    "| 邻近学校的学生-老师比例 | 15：1 | 22：1 | 12：1 |\n",
    "\n",
    "* 你会建议每位客户的房屋销售的价格为多少？\n",
    "* 从房屋特征的数值判断，这样的价格合理吗？为什么？\n",
    "\n",
    "**提示：**用你在**分析数据**部分计算出来的统计信息来帮助你证明你的答案。\n",
    "\n",
    "运行下列的代码区域，使用你优化的模型来为每位客户的房屋价值做出预测。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted selling price for Client 1's home: $391,183.33\n",
      "Predicted selling price for Client 2's home: $189,123.53\n",
      "Predicted selling price for Client 3's home: $942,666.67\n"
     ]
    }
   ],
   "source": [
    "# Produce a matrix for client data\n",
    "client_data = [[5, 17, 15], # Client 1\n",
    "               [4, 32, 22], # Client 2\n",
    "               [8, 3, 12]]  # Client 3\n",
    "\n",
    "# Show predictions\n",
    "for i, price in enumerate(reg.predict(client_data)):\n",
    "    print(\"Predicted selling price for Client {}'s home: ${:,.2f}\".format(i+1, price))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 10 - 回答：\n",
    "1. 客户1建议房屋销售价格为391183.33dollars，客户2建议销售价格为189123.53dollars，客户2建议销售价格为942666.67dollars；\n",
    "2. 分析数据部分我们得知整体房屋销售价格在105000~1024800dollars之间，房间总数越高价格相对也越高，贫困指数越低理论房屋价格将越高，学生-老师占比的值与房屋预测值也符合数值判断。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习 5\n",
    "你刚刚预测了三个客户的房子的售价。在这个练习中，你将用你的最优模型在整个测试数据上进行预测, 并计算相对于目标变量的决定系数 $R^2$ 的值。\n",
    "\n",
    "**提示：**\n",
    "* 你可能需要用到 `X_test`, `y_test`, `optimal_reg`, `performance_metric`。\n",
    "* 参考问题10的代码进行预测。\n",
    "* 参考问题2的代码来计算R^2的值。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal model has R^2 score 0.77 on test data\n"
     ]
    }
   ],
   "source": [
    "# TODO Calculate the r2 score between 'y_true' and 'y_predict'\n",
    "y_predicted = reg.predict(X_test)\n",
    "r2 = performance_metric(y_test, y_predicted)\n",
    "\n",
    "print(\"Optimal model has R^2 score {:,.2f} on test data\".format(r2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题11 - 分析决定系数\n",
    "\n",
    "你刚刚计算了最优模型在测试集上的决定系数，你会如何评价这个结果？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题11 - 回答\n",
    "\n",
    "由上可知，最优模型在测试集的决定系数为0.77,Test数据集中目标函数有77%可以用最优模型的特征进行解释。模型结果不是特别理想。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 模型健壮性\n",
    "\n",
    "一个最优的模型不一定是一个健壮模型。有的时候模型会过于复杂或者过于简单，以致于难以泛化新增添的数据；有的时候模型采用的学习算法并不适用于特定的数据结构；有的时候样本本身可能有太多噪点或样本过少，使得模型无法准确地预测目标变量。这些情况下我们会说模型是欠拟合的。\n",
    "\n",
    "### 问题 12 - 模型健壮性\n",
    "\n",
    "模型是否足够健壮来保证预测的一致性？\n",
    "\n",
    "**提示**: 执行下方区域中的代码，采用不同的训练和测试集执行 `fit_model` 函数10次。注意观察对一个特定的客户来说，预测是如何随训练数据的变化而变化的。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Trial 1: $391,183.33\n",
      "Trial 2: $411,417.39\n",
      "Trial 3: $415,800.00\n",
      "Trial 4: $420,622.22\n",
      "Trial 5: $413,334.78\n",
      "Trial 6: $411,931.58\n",
      "Trial 7: $390,250.00\n",
      "Trial 8: $407,232.00\n",
      "Trial 9: $402,531.82\n",
      "Trial 10: $413,700.00\n",
      "\n",
      "Range in prices: $30,372.22\n"
     ]
    }
   ],
   "source": [
    "vs.PredictTrials(features, prices, fit_model, client_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 12 - 回答：\n",
    "\n",
    "采用不同训练和测试集执行fit_model函数10次,客户1房屋价格的预测值在391183-423300dollars之间进行波动，价格波动范围为32116.67dollars，10次预测的标准差为9772，模型足够健壮保证预测一致性。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 13 - 实用性探讨\n",
    "*简单地讨论一下你建构的模型能否在现实世界中使用？* \n",
    "\n",
    "提示：回答以下几个问题，并给出相应结论的理由：\n",
    "- *1978年所采集的数据，在已考虑通货膨胀的前提下，在今天是否仍然适用？*\n",
    "- *数据中呈现的特征是否足够描述一个房屋？*\n",
    "- *在波士顿这样的大都市采集的数据，能否应用在其它乡镇地区？*\n",
    "- *你觉得仅仅凭房屋所在社区的环境来判断房屋价值合理吗？*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 13 - 回答：\n",
    "\n",
    "1. 模型通过对房屋三个特征，房间数量、贫困人口占比、学生/教师比预测房屋价格，考虑了通货膨胀后，其价格波动与三个特性的相关性并没有发生该表，因此仍然是适用的；\n",
    "2. 数据中仅包含三个特性，房屋特征还包含，交通状况、房屋类型等因素影响，仅三个特征是不足够描述房屋状况；\n",
    "3. 城市采集数据不能应用与乡镇地区，不同地区房屋价格趋势是不同的，特征相对最终价格的关系存在很大差异；\n",
    "4. 仅凭借社区环境判断房屋价格不合理，房屋价格还与社区所处地理位置，周边配套设施等因素相关。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 第七步.完成和提交"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "当你完成了以上所有的代码和问题，你需要将 iPython Notebook 导出 HTML，导出方法：在左上角的菜单中选择 **File -> Download as -> HTML (.html)**。当你提交项目时，需要包含**可运行的 .ipynb 文件**和**导出的 HTML 文件**。"
   ]
  }
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